Since there is more than one crack in each specimen, and since this is the case in general in structures, there is the possibility of interactions between cracks. These interactions take the form of cracks coalescing, which leads to longer cracks becoming established. While there is ongoing debate as to how these interactions are significant within the context of overall reliability, in general, in this case we felt that it would be useful to model this effect directly.
A study of reliability in a very different situation, on the application to orthopaedic hip replacements, led to some insight on other methods of damage accumulation. In particular, it was clear that a large family of short cracks cause as much damage as a single long crack.
For the specimen data, a number of approaches were made at modelling the effect of coalescence. The effect was modelled in two distinct stages. Firstly the rate of coalescence was modelled and then the growth and coalescence models were combined. Again the analysis was carried through in a Bayesian framework.